Proposed Canon

As Commanders, Warlords also control their stacks in combat, allowing for directed attacks (or preventing combat, as opposed to an unled stack, which must auto-attack when in contact with non-allied units.Erf-b1-p040a

The warlord special grants a strong drive. When a warlord enters combat or faces an enemy, it helps them focus and make decisions quickly. Some warlords learn to apply this drive at will for non-combat related activities, such as diplomacy.

A warlord's experience gain is as dependant on them learning how to connect with people as it is on actually learning how to fight.

Terminology

Every unit with Leadership is a Warlord, but can also be called a Commander, and the terms are sometimes used interchangeably.Erf-b1-p040a Another alternate term for a female warlord is 'Warlady'.

However, Warlord is a specific term for leaders with the Leadership ability. Commander is a more general term, and also encompasses Casters, who do not have Leadership.Erf-b1-p084a Both CastersErf-b1-p017 and WarlordsErf-b1-p007 can be and have been called "Commander," even insisting on it,Erf-b1-p083 while both have also been referred to with their more specific terms. (Incidentally, Wanda Firebaugh was once referred to as "officer,"Erf-b1-p005, which we can only assume is a rarely-used synonym.)

Usage as Leaders

Warlords are almost universally chosen over Casters to lead stacks; there are several reasons for this.

Warlords are more common than Casters and therefore more expendable

Casters are hard to replace

Warlords may be, in general, more competent fighters

Casters may have more tactical value elsewhere

Warlords offer Leadership bonus to their troops, making them more effective

Casters don't have leadership and generally offer no bonus to troops

An exception to this commonly accepted usage of Warlords to lead stacks comes when a caster leads a particular kind of unit, such as ones that have been created using their discipline of magic, such as when a Dirtamancer leads a stack of golems, or uncroaked are led by a Croakamancer.Erf-b1-p084a These special bonuses make these particular units (and those units only) far more effective when led by the right kind of Caster. This makes a serious case for having those Casters leading those stacks rather than a Warlord. Another good reason is if Warlords are in short supply and you need to do more than auto-attack the enemy.

Usage as City managers

A Warlord can be assigned to manage a city as its RegentTBFGK Epilogue 13. This is a temporary position that can begin or end at any time.
To have an effect, the Warlord must spend his entire turn walking around the city, observing. This prevents him from taking any other meaningful actions that turn, such as fighting, strategizing actively, training, etc.

It should be noted that this takes the Warlord's time and effort during the side's turn; the remainder of the day (or other sides' turns) the Warlord is free to do as he wishes; so he has time to eat, read, converse, relax, etc. and could defend the city against attack, but cannot leave (as movement must occur on his own turn, when he is busy doing rounds).

In the case of flying, it may be unique to sides which are known for being air powers. Dance Fighting and Rocking Out may be a learnt special. And forest-capable may be unique to Rangers, which may or may not be a different class that can be promoted to warlord. Parson Gottis' casting ability and Heavy special are likely very atypical and due to the Summon Perfect Warlord Spell.

Speculation

Ruler seems to be a separate Class of Unit. It is unclear whether a Ruler counts as a Commander.

Stanley, a Ruler, commanded a stack of dwagons and when he left that stack, they lost his Leadership.Erf-b1-p115 It is unclear whether that referred to the Leadership bonus, or the ability to make targeted attacks when led by a Commander. In this case, likely both. It is also not clear whether all Rulers have a Leadership bonus, or if Stanley retained his from his time as a Warlord and Chief Warlord.

Neither of the two non-Royal sides we have so far seen, Gobwin Knob and Charlescomm, seems to pop new warlords. Stanley promoted his warlords, and Charlie does not use warlords. While this suggests that perhaps non-Royal sides cannot pop new Warlords, but must capture or promote them instead, we know this to be false, as in LIAB Text 2, it is shown that the re-popped cities "popped the same kinds of units the capital did", including warlords. It is likely that the rate at which Stanley lost his Warlords prevented him from popping new ones at the rate he lost them, so he promoted units in the ranks to Warlord. Moreover, Stanley might choose to promote warlords rather than pop them because he himself was promoted to Warlord.